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A "hardcore" mathematics question

  • #1
  • First Post: Apr 2, 2010 11:52am Apr 2, 2010 11:52am
Need help with this probability calcuation. Any strong mathematicans here? Cheers!

Imagine there is a game and the gambler has a prob. of P1 in winning one unit of capital in a trial and 1 - P1 in lossing one unit.
He wants to know the prob. of HAVING EVER lossing more than or equal to a threshold no. of units (drawdown threshold) after a number of trials.

For example, if his prob. winning 1 unit is 0.6 and lossing 1 unit is 0.4, what is his probability of having ever lossing more than or equal to 10 units after 30 trials?
  • #2
  • Apr 2, 2010 12:02pm Apr 2, 2010 12:02pm
bout tree fiddy.

On a more serious note, this might help. http://en.wikipedia.org/wiki/Probability_distribution.
  • #3
  • Apr 2, 2010 12:09pm Apr 2, 2010 12:09pm
One of my first choices would be to get FXPetra's attention.

(bump)
  • #4
  • Apr 2, 2010 12:18pm Apr 2, 2010 12:18pm
Quoting Intu
One of my first choices would be to get FXPetra's attention.

(bump)
...or Craig, Hanover, Capitalist888, or Merlin (or is it SmJones? I always get the two mixed up).
Living the adventure in my head.
  • #5
  • Apr 2, 2010 12:26pm Apr 2, 2010 12:26pm
Quoting kk007
Need help with this probability calcuation. Any strong mathematicans here? Cheers!

Imagine there is a game and the gambler has a prob. of P1 in winning one unit of capital in a trial and 1 - P1 in lossing one unit.
He wants to know the prob. of HAVING EVER lossing more than or equal to a threshold no. of units (drawdown threshold) after a number of trials.

For example, if his prob. winning 1 unit is 0.6 and lossing 1 unit is 0.4, what is his probability of having ever lossing more than or equal to 10 units after 30 trials?...
The question is ambiguous, do you mean...

1) Having a draw down of size 10 during the 30 trials (10 consecutive losses).
2) Having a total of 10 losses during 30 trials.
3) Having his capital go lower than -10 during 30 trails.

Regardless of which it is, here (http://mathworld.wolfram.com/RandomW...mensional.html) is probably a good start.
The breaking of a wave cannot explain the whole sea.
  • #6
  • Edited 1:39pm Apr 2, 2010 1:21pm | Edited 1:39pm
I think what he is asking...

With a winning trade chance of 60% and a losing trade chance of 40% on any individual trade, with an R:R of 1:1... after any series of 30 trades...

what is the chance for being down 10 or more units net within the series? The average result of many series should converge to .60(30) wins - .40(30) loss => 18-12 => net +6 units. But obviously, the probability distribution could be "whacked" in real life, over the short term of 30 trades.

side note:
I have a link to an Equity curve similator.... unfortunately it has a few variables but not a trade length variable, it goes to about 450 trades.
Hopefully, it's legal to post the link here...if not forgive me.
http://www.hquotes.com/tradehard/simulator.html

Playing around with the above, set win/loss to 1.0 (that's 1:1 R:R), and change win prob to .6 and use lines 100. Hit generate, that's 100 trials of about 450 trades according to those settings. Ignoring Kelly value and mathematical expectation... visually estimate a quarter of the distance across the bottom horizontal axis. Let's say you have spot that is close to 100 trades. Do you have a line at or below the vertical 100 starting mark? This is a visual estimation that even with 60% win rate and 1:1 R:R, after 100 trades, you could still be negative or flat P/L. Sobering isn't it? There is a small chance even with that "edge" you wouldn't see growth until after 100 trades or so. Anyway, play with it...
  • #7
  • Apr 2, 2010 1:22pm Apr 2, 2010 1:22pm
EDIT: Posts deleted, Ive got no idea what the OP is asking.
Living the adventure in my head.
  • #8
  • Edited 2:10pm Apr 2, 2010 2:00pm | Edited 2:10pm
For simple payout (RRR = 1), binomial distribution can answer this easily.

In your case, the number of trial is 30, the number of success is at least 10 times, and the Probability of success is 40%. Key in the following into excel,

Quote
=1 - BINOMDIST(9,30,0.4,TRUE)

Then u will get the probability of lossing for at least 10times, which is about 82%.
  • #9
  • Apr 2, 2010 2:10pm Apr 2, 2010 2:10pm
Quoting ForexQuant
For simple payout (RRR = 1), binomial distribution can answer this easily.

In your case, the number of trial is 30, the number of success is at least 10 times, and the Probability of success is 40%. Key in the following into excel,



Then u will get the probability of lossing for at least 10times, which is about 29%.
I may be completely wrong, but with a .4 probability of loss, in 30 games, 12 should be losers. If this is in fact what the OP is asking, then 10 losers in 30 games should have a probability of above 0.5. No?
Living the adventure in my head.
  • #10
  • Apr 2, 2010 2:14pm Apr 2, 2010 2:14pm
I think he meant what is the chance of the drawdown to be at least 10 units after 30 trades.
The excel formula doesn't work because you consider 10 winning to be enough but you forgot to consider 10 losses at the beginning of the trial.

There's no magic formula. You must calculate every possible permutation of winning and losses which is some N. For every permutation you must calculate if it goes to 10 DD, the sum of them being some M. The exact result is of course M / N.

As it is very hard your only chance is to generate a few million permutations and find the result. It will not be the exact result but you'll have an idea after a few trials.

I don't know what you try to discover here but 30 trades are not enough to offer a realistical expectation. You need at least 1000 to know how you adjust your MM.
  • #11
  • Apr 2, 2010 2:20pm Apr 2, 2010 2:20pm
82,4%
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  • #12
  • Apr 2, 2010 2:21pm Apr 2, 2010 2:21pm
That is great stuff, but...

I still believe his original question pertains to the possibility of a loss of 10 or more units of trading capital during a sequence of 30 trades with those parameters. So what is the probability that he will be down 10 units, not lose 10 trades during a 30 trade sequence. I may have misunderstood.


For example:

Assumes he has $1000 account. He trades with a 60% win rate and 40% losing rate RRR 1:1. He bets $100 every trade. Every 30 trades he resets his account to $1000 somehow. What are the chances he will blow up (lose all $1000) in some 30 trade sequence?

I think that is what he wants to know...

(Similar to what Sauron posted above) We are all replying at the same time it seems.
  • #13
  • Apr 2, 2010 2:25pm Apr 2, 2010 2:25pm
Quoting Intu
That is great stuff, but...

I still believe his original question pertains to the possibility of a loss of 10 or more units of trading capital during a sequence of 30 trades with those parameters. So what is the probability that he will be down 10 units, not lose 10 trades during a 30 trade sequence. I may have misunderstood.


For example:

Assumes he has $1000 account. He trades with a 60% win rate and 40% losing rate RRR 1:1. He bets $100 every trade. Every 30 trades he resets his account to $1000 somehow. What are the...
That makes sense... this is a fun thread .
Living the adventure in my head.
  • #14
  • Apr 2, 2010 2:26pm Apr 2, 2010 2:26pm
Look brah. There lots of martingale and hedging systems and EAs. There are people ahead of you by decades! Don't try to invent the wheel. Yes hedging and Martingale systems can work. But there lots of systems ,like Blessing ,10P3 ,Fxtradepro..etc. Google this stuff
  • #15
  • Apr 2, 2010 2:31pm Apr 2, 2010 2:31pm
Maybe I should explain a bit.

BINOMDIST(9,30,0.4,TRUE) means the cumulative probability of losing (Known as probability of success in statistic jargon) for 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 times out of 30 trials. Since kk wanted to know what is the probability of losing at least 10times, so we just deducted BINOMDIST(9,30,0.4,TRUE) from 100%.

It may be hard for me to explain further, so just check this out http://en.wikipedia.org/wiki/Binomial_distribution
  • #16
  • Apr 2, 2010 2:41pm Apr 2, 2010 2:41pm
Quoting Intu
That is great stuff, but...

So what is the probability that he will be down 10 units, not lose 10 trades during a 30 trade sequence.
ops my bad, i think i misunderstood the question. But then this can be still answer by binomial distribution.
  • #17
  • Edited 2:48pm Apr 2, 2010 2:48pm | Edited 2:48pm
You are a much better mathematician than I, I like your explanations.

May I ask how hard would it be to compute the chances of having 10 more losses than wins at any time in a sequence of up to 30 trades?

Initially, this is what I thought he was asking. It's an ugly permutation problem I imagine, as Sauron suggested.

(I just saw your post above)
  • #18
  • Apr 2, 2010 2:48pm Apr 2, 2010 2:48pm
It is a Binomial Distribution of some sort, depending on what the OP actually meant. If anybody actually cares to dig though the link I posted, the result which is derived is quite general, more so, the formula has something quite interesting to say on the nature of markets in general (hint: you can also measure the average deviation of market data from a starting point, how does this compare to the result in the link?).
The breaking of a wave cannot explain the whole sea.
  • #19
  • Apr 2, 2010 2:50pm Apr 2, 2010 2:50pm
LossTrades + WinTrades = 30

LossTrades - WinTrades >= 10

Solve the above equations then we know Loss >= 20 so that we can have at least 10 unit of losses.

so the cumulative probabability from 0 to 19 losses is BINOMDIST(9,30,0.4,TRUE), which is about 99.7%, so the cumulative probability from 20 to 30 losses is 100 - 99.7 = 0.3%

Anyone else can verify this?
  • #20
  • Apr 2, 2010 8:53pm Apr 2, 2010 8:53pm
The question has been clearly state, but it is not that easy to understand at the first sight. The question is very close to third option below. The keyword "having ever" should be noticed. The third option should be modified to "Having his captial even been to or lower than -10 during the 30 trials"
Anyway, thanks for your link.

Quoting Craig
The question is ambiguous, do you mean...

1) Having a draw down of size 10 during the 30 trials (10 consecutive losses).
2) Having a total of 10 losses during 30 trials.
3) Having his capital go lower than -10 during 30 trails.

Regardless of which it is, here (http://mathworld.wolfram.com/RandomW...mensional.html) is probably a good start.
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